Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(369,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} - 20 x^{3} + 64 x^{2} - 32 x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.2 | ||
Root | \(0.285770 - 0.285770i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.369 |
Dual form | 920.2.e.b.369.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(281\) | \(461\) | \(737\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.49931i | − | 1.44298i | −0.692425 | − | 0.721490i | \(-0.743458\pi\) | ||
0.692425 | − | 0.721490i | \(-0.256542\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.11714 | − | 0.719533i | 0.946813 | − | 0.321785i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.92777i | − | 1.10659i | −0.832984 | − | 0.553297i | \(-0.813369\pi\) | ||
0.832984 | − | 0.553297i | \(-0.186631\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.24657 | −1.08219 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.10909 | −1.23894 | −0.619468 | − | 0.785022i | \(-0.712652\pi\) | ||||
−0.619468 | + | 0.785022i | \(0.712652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.0122971i | − | 0.00341059i | −0.999999 | − | 0.00170530i | \(-0.999457\pi\) | ||
0.999999 | − | 0.00170530i | \(-0.000542813\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.79834 | − | 5.29139i | −0.464329 | − | 1.36623i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.155378i | − | 0.0376847i | −0.999822 | − | 0.0188424i | \(-0.994002\pi\) | ||
0.999822 | − | 0.0188424i | \(-0.00599807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.32471 | −0.992158 | −0.496079 | − | 0.868277i | \(-0.665227\pi\) | ||||
−0.496079 | + | 0.868277i | \(0.665227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.31743 | −1.59679 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.96454 | − | 3.04670i | 0.792909 | − | 0.609340i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.616262i | 0.118600i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.79978 | 1.26269 | 0.631344 | − | 0.775503i | \(-0.282504\pi\) | ||||
0.631344 | + | 0.775503i | \(0.282504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.20713 | 0.396412 | 0.198206 | − | 0.980160i | \(-0.436489\pi\) | ||||
0.198206 | + | 0.980160i | \(0.436489\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.2699i | 1.78776i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.10663 | − | 6.19850i | −0.356085 | − | 1.04774i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.60741i | 0.757453i | 0.925509 | + | 0.378726i | \(0.123638\pi\) | ||||
−0.925509 | + | 0.378726i | \(0.876362\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0307342 | −0.00492142 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.67826 | −1.19914 | −0.599571 | − | 0.800321i | \(-0.704662\pi\) | ||||
−0.599571 | + | 0.800321i | \(0.704662\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.38997i | 1.27946i | 0.768600 | + | 0.639729i | \(0.220954\pi\) | ||||
−0.768600 | + | 0.639729i | \(0.779046\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.87344 | + | 2.33602i | −1.02463 | + | 0.348233i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.38116i | − | 0.930787i | −0.885104 | − | 0.465394i | \(-0.845913\pi\) | ||
0.885104 | − | 0.465394i | \(-0.154087\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.57186 | −0.224551 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.388339 | −0.0543783 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.80358i | − | 1.07190i | −0.844248 | − | 0.535952i | \(-0.819953\pi\) | ||
0.844248 | − | 0.535952i | \(-0.180047\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.69951 | + | 2.95662i | −1.17304 | + | 0.398671i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.8088i | 1.43166i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1275 | 1.83924 | 0.919622 | − | 0.392805i | \(-0.128495\pi\) | ||||
0.919622 | + | 0.392805i | \(0.128495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.05297 | 0.903040 | 0.451520 | − | 0.892261i | \(-0.350882\pi\) | ||||
0.451520 | + | 0.892261i | \(0.350882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.50523i | 1.19755i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.00884814 | − | 0.0260346i | −0.00109748 | − | 0.00322919i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.31363i | − | 0.893502i | −0.894658 | − | 0.446751i | \(-0.852581\pi\) | ||
0.894658 | − | 0.446751i | \(-0.147419\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.49931 | −0.300882 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.84061 | −0.693153 | −0.346576 | − | 0.938022i | \(-0.612656\pi\) | ||||
−0.346576 | + | 0.938022i | \(0.612656\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.727674i | 0.0851678i | 0.999093 | + | 0.0425839i | \(0.0135590\pi\) | ||||
−0.999093 | + | 0.0425839i | \(0.986441\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.61466 | − | 9.90864i | −0.879266 | − | 1.14415i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0305i | 1.37100i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.81003 | −0.541171 | −0.270586 | − | 0.962696i | \(-0.587217\pi\) | ||||
−0.270586 | + | 0.962696i | \(0.587217\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.19948 | −0.911054 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.75797i | 0.851548i | 0.904830 | + | 0.425774i | \(0.139998\pi\) | ||||
−0.904830 | + | 0.425774i | \(0.860002\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.111800 | − | 0.328957i | −0.0121264 | − | 0.0356804i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 16.9948i | − | 1.82203i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.77560 | −0.718212 | −0.359106 | − | 0.933297i | \(-0.616918\pi\) | ||||
−0.359106 | + | 0.933297i | \(0.616918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0360030 | −0.00377414 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 5.51631i | − | 0.572014i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.15602 | + | 3.11177i | −0.939388 | + | 0.319261i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.8705i | − | 1.50987i | −0.655799 | − | 0.754935i | \(-0.727668\pi\) | ||
0.655799 | − | 0.754935i | \(-0.272332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.3405 | 1.34077 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.0023 | −1.29378 | −0.646889 | − | 0.762584i | \(-0.723930\pi\) | ||||
−0.646889 | + | 0.762584i | \(0.723930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.85814i | − | 0.183088i | −0.995801 | − | 0.0915442i | \(-0.970820\pi\) | ||
0.995801 | − | 0.0915442i | \(-0.0291803\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.4920 | + | 5.26513i | −1.51186 | + | 0.513824i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.471267i | − | 0.0455591i | −0.999741 | − | 0.0227795i | \(-0.992748\pi\) | ||
0.999741 | − | 0.0227795i | \(-0.00725158\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.83022 | 0.175303 | 0.0876515 | − | 0.996151i | \(-0.472064\pi\) | ||||
0.0876515 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.5154 | 1.09299 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.81151i | 0.734845i | 0.930054 | + | 0.367422i | \(0.119760\pi\) | ||||
−0.930054 | + | 0.367422i | \(0.880240\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.719533 | − | 2.11714i | −0.0670968 | − | 0.197424i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0399233i | 0.00369091i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.454912 | −0.0417017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.88461 | 0.534964 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.1904i | 1.73034i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.20129 | − | 9.30291i | 0.554660 | − | 0.832077i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.62237i | 0.676376i | 0.941079 | + | 0.338188i | \(0.109814\pi\) | ||||
−0.941079 | + | 0.338188i | \(0.890186\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.9692 | 1.84623 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.4575 | 1.70001 | 0.850007 | − | 0.526772i | \(-0.176598\pi\) | ||||
0.850007 | + | 0.526772i | \(0.176598\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.6618i | 1.09792i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.443421 | + | 1.30471i | 0.0381636 | + | 0.112292i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.3163i | − | 1.39399i | −0.717074 | − | 0.696997i | \(-0.754519\pi\) | ||
0.717074 | − | 0.696997i | \(-0.245481\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.9289 | 1.69035 | 0.845175 | − | 0.534490i | \(-0.179496\pi\) | ||||
0.845175 | + | 0.534490i | \(0.179496\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.9485 | −1.34311 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0505297i | 0.00422551i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.3961 | − | 4.89267i | 1.19553 | − | 0.406314i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.92857i | 0.324023i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.04540 | 0.659105 | 0.329552 | − | 0.944137i | \(-0.393102\pi\) | ||||
0.329552 | + | 0.944137i | \(0.393102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.40963 | 0.277472 | 0.138736 | − | 0.990329i | \(-0.455696\pi\) | ||||
0.138736 | + | 0.990329i | \(0.455696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.504446i | 0.0407821i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.67279 | − | 1.58810i | 0.375328 | − | 0.127559i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.1868i | 1.69089i | 0.534061 | + | 0.845446i | \(0.320665\pi\) | ||||
−0.534061 | + | 0.845446i | \(0.679335\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −19.5036 | −1.54674 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.92777 | −0.230741 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 20.9487i | − | 1.64083i | −0.571769 | − | 0.820415i | \(-0.693743\pi\) | ||
0.571769 | − | 0.820415i | \(-0.306257\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.38953 | + | 21.7428i | 0.575274 | + | 1.69267i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 10.9861i | − | 0.850131i | −0.905163 | − | 0.425065i | \(-0.860251\pi\) | ||
0.905163 | − | 0.425065i | \(-0.139749\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9998 | 0.999988 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.0405 | 1.07370 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.31110i | − | 0.327767i | −0.986480 | − | 0.163884i | \(-0.947598\pi\) | ||
0.986480 | − | 0.163884i | \(-0.0524021\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.92005 | − | 11.6073i | −0.674292 | − | 0.877429i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 35.3091i | − | 2.65399i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0791 | 1.42604 | 0.713018 | − | 0.701146i | \(-0.247328\pi\) | ||||
0.713018 | + | 0.701146i | \(0.247328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.09312 | 0.304239 | 0.152120 | − | 0.988362i | \(-0.451390\pi\) | ||||
0.152120 | + | 0.988362i | \(0.451390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 17.6276i | − | 1.30307i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.31518 | + | 9.75451i | 0.243737 | + | 0.717166i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.638462i | 0.0466890i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.80428 | 0.131242 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.21032 | 0.449363 | 0.224682 | − | 0.974432i | \(-0.427866\pi\) | ||||
0.224682 | + | 0.974432i | \(0.427866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 13.2674i | − | 0.955005i | −0.878630 | − | 0.477503i | \(-0.841542\pi\) | ||
0.878630 | − | 0.477503i | \(-0.158458\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0650686 | + | 0.0221143i | −0.00465966 | + | 0.00158364i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.8836i | 0.989163i | 0.869131 | + | 0.494582i | \(0.164679\pi\) | ||||
−0.869131 | + | 0.494582i | \(0.835321\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.8004 | 1.61628 | 0.808139 | − | 0.588992i | \(-0.200475\pi\) | ||||
0.808139 | + | 0.588992i | \(0.200475\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.2791 | −1.28931 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 19.9082i | − | 1.39728i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.2559 | + | 5.52476i | −1.13536 | + | 0.385866i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.24657i | 0.225652i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.7706 | 1.22922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.698944 | −0.0481173 | −0.0240587 | − | 0.999711i | \(-0.507659\pi\) | ||||
−0.0240587 | + | 0.999711i | \(0.507659\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.5975i | 1.00021i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.03686 | + | 17.7627i | 0.411711 | + | 1.21141i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.46197i | − | 0.438667i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.81869 | 0.122895 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.00191069 | −0.000128527 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.3719i | 1.83296i | 0.400082 | + | 0.916480i | \(0.368982\pi\) | ||||
−0.400082 | + | 0.916480i | \(0.631018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.8712 | + | 9.89134i | −0.858079 | + | 0.659422i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.6070i | 0.704011i | 0.935998 | + | 0.352005i | \(0.114500\pi\) | ||||
−0.935998 | + | 0.352005i | \(0.885500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.11433 | −0.205801 | −0.102900 | − | 0.994692i | \(-0.532812\pi\) | ||||
−0.102900 | + | 0.994692i | \(0.532812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 30.0680 | 1.97833 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 23.5295i | − | 1.54147i | −0.637156 | − | 0.770735i | \(-0.719889\pi\) | ||
0.637156 | − | 0.770735i | \(-0.280111\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.59145 | − | 13.5098i | −0.299513 | − | 0.881281i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.0218i | 0.780899i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.4214 | −1.57969 | −0.789844 | − | 0.613308i | \(-0.789838\pi\) | ||||
−0.789844 | + | 0.613308i | \(0.789838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.5525 | 1.77481 | 0.887407 | − | 0.460986i | \(-0.152504\pi\) | ||||
0.887407 | + | 0.460986i | \(0.152504\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3419i | 1.43323i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.32784 | + | 1.13101i | −0.212608 | + | 0.0722573i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0531813i | 0.00338385i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.3896 | 1.22877 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.3692 | −1.60129 | −0.800645 | − | 0.599139i | \(-0.795510\pi\) | ||||
−0.800645 | + | 0.599139i | \(0.795510\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.10909i | 0.258336i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.822167 | + | 0.279423i | −0.0514861 | + | 0.0174981i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.8501i | 1.23822i | 0.785306 | + | 0.619108i | \(0.212506\pi\) | ||||
−0.785306 | + | 0.619108i | \(0.787494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.4894 | 0.838193 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.0760 | −1.36647 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.9087i | − | 1.41261i | −0.707906 | − | 0.706306i | \(-0.750360\pi\) | ||
0.707906 | − | 0.706306i | \(-0.249640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.61493 | − | 16.5213i | −0.344923 | − | 1.01489i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9344i | 1.03637i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.03048 | −0.0628295 | −0.0314148 | − | 0.999506i | \(-0.510001\pi\) | ||||
−0.0314148 | + | 0.999506i | \(0.510001\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.79576 | −0.230576 | −0.115288 | − | 0.993332i | \(-0.536779\pi\) | ||||
−0.115288 | + | 0.993332i | \(0.536779\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0899829i | 0.00544601i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.2907 | + | 12.5192i | −0.982364 | + | 0.754934i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.48782i | − | 0.0893946i | −0.999001 | − | 0.0446973i | \(-0.985768\pi\) | ||
0.999001 | − | 0.0446973i | \(-0.0142323\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.16560 | −0.428993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2796 | −0.613228 | −0.306614 | − | 0.951834i | \(-0.599196\pi\) | ||||
−0.306614 | + | 0.951834i | \(0.599196\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.62427i | 0.274884i | 0.990510 | + | 0.137442i | \(0.0438881\pi\) | ||||
−0.990510 | + | 0.137442i | \(0.956112\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.77730 | + | 22.8838i | 0.460688 | + | 1.35552i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.4802i | 1.32697i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9759 | 0.998580 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.1661 | −2.17871 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 16.3067i | − | 0.952650i | −0.879269 | − | 0.476325i | \(-0.841969\pi\) | ||
0.879269 | − | 0.476325i | \(-0.158031\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.9099 | − | 10.1652i | 1.74142 | − | 0.591841i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.53228i | − | 0.146938i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0122971 | −0.000711158 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.5639 | 1.41584 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.4969i | 1.86690i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.9321 | − | 5.07484i | 0.855010 | − | 0.290585i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.28659i | 0.530014i | 0.964246 | + | 0.265007i | \(0.0853743\pi\) | ||||
−0.964246 | + | 0.265007i | \(0.914626\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.64409 | −0.264193 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.3713 | −1.38197 | −0.690984 | − | 0.722870i | \(-0.742822\pi\) | ||||
−0.690984 | + | 0.722870i | \(0.742822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 15.0048i | − | 0.848119i | −0.905634 | − | 0.424060i | \(-0.860605\pi\) | ||
0.905634 | − | 0.424060i | \(-0.139395\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.83933 | + | 20.1239i | 0.385352 | + | 1.13385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7.84747i | − | 0.440758i | −0.975414 | − | 0.220379i | \(-0.929271\pi\) | ||
0.975414 | − | 0.220379i | \(-0.0707294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.9409 | −1.56439 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.17784 | −0.0657408 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.671966i | 0.0373892i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0374655 | − | 0.0487523i | −0.00207821 | − | 0.00270429i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4.57429i | − | 0.252959i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.6826 | −1.03000 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.28156 | 0.510160 | 0.255080 | − | 0.966920i | \(-0.417898\pi\) | ||||
0.255080 | + | 0.966920i | \(0.417898\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 14.9583i | − | 0.819709i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.26240 | − | 15.4840i | −0.287515 | − | 0.845979i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.3760i | 1.43679i | 0.695634 | + | 0.718397i | \(0.255124\pi\) | ||||
−0.695634 | + | 0.718397i | \(0.744876\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.5234 | 1.06037 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.06928 | −0.491129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.8924i | − | 0.858107i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.29139 | + | 1.79834i | −0.284879 | + | 0.0968193i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3316i | 0.984093i | 0.870569 | + | 0.492047i | \(0.163751\pi\) | ||||
−0.870569 | + | 0.492047i | \(0.836249\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.2759 | 1.72769 | 0.863845 | − | 0.503758i | \(-0.168050\pi\) | ||||
0.863845 | + | 0.503758i | \(0.168050\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.00757822 | 0.000404495 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.5653i | − | 1.57360i | −0.617208 | − | 0.786800i | \(-0.711736\pi\) | ||
0.617208 | − | 0.786800i | \(-0.288264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.3654 | + | 4.20251i | −0.656286 | + | 0.223046i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.13697i | 0.0601747i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.4169 | −1.76368 | −0.881838 | − | 0.471552i | \(-0.843694\pi\) | ||||
−0.881838 | + | 0.471552i | \(0.843694\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.296842 | −0.0156232 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 14.7075i | − | 0.771943i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.523585 | + | 1.54059i | 0.0274057 | + | 0.0806379i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.4764i | 1.32986i | 0.746908 | + | 0.664928i | \(0.231538\pi\) | ||||
−0.746908 | + | 0.664928i | \(0.768462\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.9280 | 1.29770 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.8471 | −1.18616 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.28172i | − | 0.169921i | −0.996384 | − | 0.0849605i | \(-0.972924\pi\) | ||
0.996384 | − | 0.0849605i | \(-0.0270764\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.2509 | − | 15.4990i | −1.20067 | − | 0.800363i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.0836174i | − | 0.00430651i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.66762 | −0.291126 | −0.145563 | − | 0.989349i | \(-0.546499\pi\) | ||||
−0.145563 | + | 0.989349i | \(0.546499\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.0507 | 0.975997 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.4343i | 1.75951i | 0.475428 | + | 0.879755i | \(0.342293\pi\) | ||||
−0.475428 | + | 0.879755i | \(0.657707\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.65633 | + | 25.4702i | 0.441167 | + | 1.29808i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 27.2387i | − | 1.38462i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.3737 | 0.728773 | 0.364387 | − | 0.931248i | \(-0.381279\pi\) | ||||
0.364387 | + | 0.931248i | \(0.381279\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.155378 | −0.00785781 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 48.6305i | − | 2.45309i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1835 | + | 3.46098i | −0.512388 | + | 0.174141i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.6149i | 0.733500i | 0.930319 | + | 0.366750i | \(0.119530\pi\) | ||||
−0.930319 | + | 0.366750i | \(0.880470\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 31.6458 | 1.58427 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.65553 | −0.182548 | −0.0912742 | − | 0.995826i | \(-0.529094\pi\) | ||||
−0.0912742 | + | 0.995826i | \(0.529094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.0271412i | − | 0.00135200i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.3594 | + | 5.89980i | −0.862597 | + | 0.293163i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.9322i | − | 0.938436i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.40926 | −0.218024 | −0.109012 | − | 0.994040i | \(-0.534769\pi\) | ||||
−0.109012 | + | 0.994040i | \(0.534769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −40.7795 | −2.01150 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 41.3621i | − | 2.03530i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.58212 | + | 16.4247i | 0.274015 | + | 0.806257i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 49.8087i | − | 2.43914i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.5906 | −1.59216 | −0.796078 | − | 0.605195i | \(-0.793095\pi\) | ||||
−0.796078 | + | 0.605195i | \(0.793095\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.23954 | 0.206622 | 0.103311 | − | 0.994649i | \(-0.467056\pi\) | ||||
0.103311 | + | 0.994649i | \(0.467056\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.7169i | 1.00729i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.473391 | − | 0.616003i | −0.0229628 | − | 0.0298806i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 20.6495i | − | 0.999299i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.126290 | 0.00609732 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.81123 | 0.0872436 | 0.0436218 | − | 0.999048i | \(-0.486110\pi\) | ||||
0.0436218 | + | 0.999048i | \(0.486110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.76263i | − | 0.0847068i | −0.999103 | − | 0.0423534i | \(-0.986514\pi\) | ||
0.999103 | − | 0.0423534i | \(-0.0134855\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.2283 | − | 35.9803i | −0.586303 | − | 1.72512i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.32471i | 0.206879i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7848 | 1.27837 | 0.639184 | − | 0.769054i | \(-0.279272\pi\) | ||||
0.639184 | + | 0.769054i | \(0.279272\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.10316 | 0.243008 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.6631i | 0.791686i | 0.918318 | + | 0.395843i | \(0.129548\pi\) | ||||
−0.918318 | + | 0.395843i | \(0.870452\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3449 | + | 4.87527i | −0.680012 | + | 0.231110i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 20.1080i | − | 0.951075i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.1236 | 1.61039 | 0.805196 | − | 0.593008i | \(-0.202060\pi\) | ||||
0.805196 | + | 0.593008i | \(0.202060\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.5507 | 1.48566 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 8.52174i | − | 0.400386i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0762234 | + | 0.0259054i | −0.00357341 | + | 0.00121446i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.5980i | 1.15065i | 0.817926 | + | 0.575324i | \(0.195124\pi\) | ||||
−0.817926 | + | 0.575324i | \(0.804876\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0957537 | 0.00446940 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.7297 | −0.499733 | −0.249866 | − | 0.968280i | \(-0.580387\pi\) | ||||
−0.249866 | + | 0.968280i | \(0.580387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 22.3124i | − | 1.03695i | −0.855094 | − | 0.518473i | \(-0.826501\pi\) | ||
0.855094 | − | 0.518473i | \(-0.173499\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.96917 | − | 11.6788i | −0.184066 | − | 0.541591i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.0218i | 0.926497i | 0.886229 | + | 0.463248i | \(0.153316\pi\) | ||||
−0.886229 | + | 0.463248i | \(0.846684\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.4127 | −0.988744 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 52.9525 | 2.43992 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 34.4751i | − | 1.58517i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.1455 | + | 13.1761i | −0.786691 | + | 0.604561i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.3349i | 1.16001i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.61905 | 0.348123 | 0.174062 | − | 0.984735i | \(-0.444311\pi\) | ||||
0.174062 | + | 0.984735i | \(0.444311\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0566576 | 0.00258336 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.31743i | 0.332954i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.6998 | − | 31.4829i | −0.485854 | − | 1.42956i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 21.5163i | − | 0.974997i | −0.873124 | − | 0.487499i | \(-0.837909\pi\) | ||
0.873124 | − | 0.487499i | \(-0.162091\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −52.3574 | −2.36768 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.3705 | −0.468015 | −0.234007 | − | 0.972235i | \(-0.575184\pi\) | ||||
−0.234007 | + | 0.972235i | \(0.575184\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.05654i | − | 0.0475841i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.2436 | − | 9.59890i | 1.26945 | − | 0.431438i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.1000i | 0.767039i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.2850 | 0.729018 | 0.364509 | − | 0.931200i | \(-0.381237\pi\) | ||||
0.364509 | + | 0.931200i | \(0.381237\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.4577 | −1.22672 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9326i | 0.754986i | 0.926012 | + | 0.377493i | \(0.123214\pi\) | ||||
−0.926012 | + | 0.377493i | \(0.876786\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.5277 | + | 9.35559i | −1.22497 | + | 0.416318i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 32.4907i | − | 1.44296i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −39.0075 | −1.72898 | −0.864488 | − | 0.502654i | \(-0.832357\pi\) | ||||
−0.864488 | + | 0.502654i | \(0.832357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.13046 | 0.0942462 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.66516i | − | 0.117670i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.33700 | − | 3.93395i | −0.0589151 | − | 0.173350i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.2207i | 1.15319i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.7748 | −0.472961 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.1380 | 1.45180 | 0.725902 | − | 0.687798i | \(-0.241423\pi\) | ||||
0.725902 | + | 0.687798i | \(0.241423\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.4056i | 0.542460i | 0.962515 | + | 0.271230i | \(0.0874304\pi\) | ||||
−0.962515 | + | 0.271230i | \(0.912570\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −29.0103 | + | 22.2940i | −1.26611 | + | 0.972990i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 0.342939i | − | 0.0149387i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −45.8660 | −1.99041 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0944201i | 0.00408979i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.339092 | − | 0.997737i | −0.0146602 | − | 0.0431359i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 47.6846i | − | 2.05774i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.45891 | 0.278205 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.53472 | −0.366936 | −0.183468 | − | 0.983026i | \(-0.558732\pi\) | ||||
−0.183468 | + | 0.983026i | \(0.558732\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 10.2300i | − | 0.439011i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.87482 | − | 1.31690i | 0.165979 | − | 0.0564099i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.45828i | − | 0.276136i | −0.990423 | − | 0.138068i | \(-0.955911\pi\) | ||
0.990423 | − | 0.138068i | \(-0.0440893\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.8980 | −0.977262 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.4071 | −1.25279 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0827i | 0.598857i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.3796 | − | 8.28568i | 1.03486 | − | 0.351708i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.08413i | 0.173050i | 0.996250 | + | 0.0865251i | \(0.0275763\pi\) | ||||
−0.996250 | + | 0.0865251i | \(0.972424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.103172 | 0.00436371 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.59572 | 0.0673713 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 15.4494i | − | 0.651114i | −0.945522 | − | 0.325557i | \(-0.894448\pi\) | ||
0.945522 | − | 0.325557i | \(-0.105552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.62064 | + | 16.5380i | 0.236462 | + | 0.695761i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.0062i | 1.00817i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.2633 | −1.77177 | −0.885886 | − | 0.463903i | \(-0.846448\pi\) | ||||
−0.885886 | + | 0.463903i | \(0.846448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.74497 | −0.114873 | −0.0574367 | − | 0.998349i | \(-0.518293\pi\) | ||||
−0.0574367 | + | 0.998349i | \(0.518293\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 15.5215i | − | 0.648422i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.04670 | − | 3.96454i | −0.127056 | − | 0.165333i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 8.93871i | − | 0.372123i | −0.982538 | − | 0.186062i | \(-0.940428\pi\) | ||
0.982538 | − | 0.186062i | \(-0.0595724\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.1593 | −1.37805 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.7136 | 0.942318 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.0656i | 1.32802i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0287261 | + | 0.0845232i | 0.00118768 | + | 0.00349460i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 5.90821i | − | 0.243858i | −0.992539 | − | 0.121929i | \(-0.961092\pi\) | ||
0.992539 | − | 0.121929i | \(-0.0389080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.54520 | −0.393303 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.6994 | 1.42734 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.8823i | 1.14499i | 0.819909 | + | 0.572494i | \(0.194024\pi\) | ||||
−0.819909 | + | 0.572494i | \(0.805976\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.963111 | + | 0.327324i | −0.0394837 | + | 0.0134190i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 56.9854i | − | 2.33226i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.5644 | −0.431648 | −0.215824 | − | 0.976432i | \(-0.569244\pi\) | ||||
−0.215824 | + | 0.976432i | \(0.569244\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.8910 | 1.46403 | 0.732013 | − | 0.681291i | \(-0.238581\pi\) | ||||
0.732013 | + | 0.681291i | \(0.238581\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.7442i | 0.966940i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.4585 | − | 4.23417i | 0.506511 | − | 0.172143i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.0640i | 1.17967i | 0.807524 | + | 0.589835i | \(0.200807\pi\) | ||||
−0.807524 | + | 0.589835i | \(0.799193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −49.7569 | −2.01625 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0784695 | −0.00317454 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.4282i | 0.986644i | 0.869847 | + | 0.493322i | \(0.164218\pi\) | ||||
−0.869847 | + | 0.493322i | \(0.835782\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.8081 | + | 40.6287i | 0.556797 | + | 1.63831i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 29.5614i | − | 1.19010i | −0.803689 | − | 0.595049i | \(-0.797133\pi\) | ||
0.803689 | − | 0.595049i | \(-0.202867\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.5880 | 1.22944 | 0.614718 | − | 0.788747i | \(-0.289270\pi\) | ||||
0.614718 | + | 0.788747i | \(0.289270\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.616262 | 0.0247298 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.8374i | 0.794769i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.43523 | − | 24.1576i | 0.257409 | − | 0.966303i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 44.4144i | − | 1.77374i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.715890 | 0.0285444 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.5713 | 0.420835 | 0.210418 | − | 0.977612i | \(-0.432518\pi\) | ||||
0.210418 | + | 0.977612i | \(0.432518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.74688i | 0.0694323i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.48455 | + | 16.1376i | 0.217648 | + | 0.640402i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0193293i | 0.000765853i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.9620 | 0.750123 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.4738 | −0.808666 | −0.404333 | − | 0.914612i | \(-0.632496\pi\) | ||||
−0.404333 | + | 0.914612i | \(0.632496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.4989i | 0.729525i | 0.931101 | + | 0.364763i | \(0.118850\pi\) | ||||
−0.931101 | + | 0.364763i | \(0.881150\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 44.3946 | − | 15.0880i | 1.74804 | − | 0.594090i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 18.6328i | − | 0.732531i | −0.930510 | − | 0.366266i | \(-0.880636\pi\) | ||
0.930510 | − | 0.366266i | \(-0.119364\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58.0511 | −2.27871 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.1505 | −0.632988 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.5290i | 1.19469i | 0.801983 | + | 0.597347i | \(0.203778\pi\) | ||||
−0.801983 | + | 0.597347i | \(0.796222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 41.1943 | − | 14.0003i | 1.60959 | − | 0.547039i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.36245i | − | 0.0921678i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.6231 | 1.03709 | 0.518545 | − | 0.855051i | \(-0.326474\pi\) | ||||
0.518545 | + | 0.855051i | \(0.326474\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.0529 | −0.507700 | −0.253850 | − | 0.967244i | \(-0.581697\pi\) | ||||
−0.253850 | + | 0.967244i | \(0.581697\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.00477543i | 0.000185462i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.11057 | + | 26.8067i | 0.353293 | + | 1.03952i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.79978i | − | 0.263289i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 68.4110 | 2.64492 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.9813 | −1.11881 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.9120i | 1.11448i | 0.830353 | + | 0.557238i | \(0.188139\pi\) | ||||
−0.830353 | + | 0.557238i | \(0.811861\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.87757 | + | 2.44320i | 0.0722676 | + | 0.0940388i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4824i | 0.479738i | 0.970805 | + | 0.239869i | \(0.0771045\pi\) | ||||
−0.970805 | + | 0.239869i | \(0.922896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.5375 | −1.67081 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.5102 | 1.01587 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.0241i | 1.53148i | 0.643150 | + | 0.765740i | \(0.277627\pi\) | ||||
−0.643150 | + | 0.765740i | \(0.722373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.7401 | − | 34.5438i | −0.448566 | − | 1.31985i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.78369i | 0.296966i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0959612 | −0.00365583 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.9938 | −1.48340 | −0.741698 | − | 0.670734i | \(-0.765979\pi\) | ||||
−0.741698 | + | 0.670734i | \(0.765979\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 39.0578i | − | 1.48368i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 42.1923 | − | 14.3395i | 1.60044 | − | 0.543929i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.19303i | 0.0451894i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −58.8077 | −2.22431 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.9042 | 0.827309 | 0.413655 | − | 0.910434i | \(-0.364252\pi\) | ||||
0.413655 | + | 0.910434i | \(0.364252\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 19.9257i | − | 0.751513i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.7652 | + | 11.4755i | −1.27167 | + | 0.432192i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.0678i | 1.43169i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.1360 | −1.20689 | −0.603447 | − | 0.797403i | \(-0.706207\pi\) | ||||
−0.603447 | + | 0.797403i | \(0.706207\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.6161 | 0.585650 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.20713i | − | 0.0826576i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0363578 | + | 0.106978i | 0.00135970 | + | 0.00400077i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 61.0367i | 2.27946i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.4018 | 0.910033 | 0.455017 | − | 0.890483i | \(-0.349633\pi\) | ||||
0.455017 | + | 0.890483i | \(0.349633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.44023 | −0.202605 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 68.8625i | − | 2.56102i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.9580 | − | 20.7169i | 1.00120 | − | 0.769407i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.8573i | 1.29279i | 0.763005 | + | 0.646393i | \(0.223723\pi\) | ||||
−0.763005 | + | 0.646393i | \(0.776277\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 31.2409 | 1.15707 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.30362 | 0.0482161 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.7343i | 1.13520i | 0.823306 | + | 0.567598i | \(0.192127\pi\) | ||||
−0.823306 | + | 0.567598i | \(0.807873\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.82674 | + | 8.31733i | 0.104266 | + | 0.306789i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.0523i | 1.10699i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.7573 | 1.42571 | 0.712855 | − | 0.701312i | \(-0.247402\pi\) | ||||
0.712855 | + | 0.701312i | \(0.247402\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.132917 | 0.00488282 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.0371i | 1.57888i | 0.613830 | + | 0.789438i | \(0.289628\pi\) | ||||
−0.613830 | + | 0.789438i | \(0.710372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0332 | − | 5.78893i | 0.624049 | − | 0.212090i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 25.1868i | − | 0.921538i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.37976 | −0.0504154 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.3761 | −1.29089 | −0.645447 | − | 0.763805i | \(-0.723329\pi\) | ||||
−0.645447 | + | 0.763805i | \(0.723329\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 63.4056i | 2.31063i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.21866 | − | 2.45334i | 0.262714 | − | 0.0892862i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.2605i | 1.86309i | 0.363621 | + | 0.931547i | \(0.381540\pi\) | ||||
−0.363621 | + | 0.931547i | \(0.618460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.2699 | 0.372774 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.4331 | −0.486950 | −0.243475 | − | 0.969907i | \(-0.578287\pi\) | ||||
−0.243475 | + | 0.969907i | \(0.578287\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 5.35846i | − | 0.193989i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.362966 | + | 1.06798i | 0.0131231 | + | 0.0386130i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.173727i | − | 0.00627291i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.7779 | 0.893512 | 0.446756 | − | 0.894656i | \(-0.352579\pi\) | ||||
0.446756 | + | 0.894656i | \(0.352579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 49.6117 | 1.78672 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.9946i | 0.431417i | 0.976458 | + | 0.215708i | \(0.0692061\pi\) | ||||
−0.976458 | + | 0.215708i | \(0.930794\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.75026 | − | 6.72446i | 0.314319 | − | 0.241550i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 33.7144i | − | 1.20950i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.2063 | 1.18974 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.9996 | 0.858772 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.19045i | 0.149755i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.2446 | + | 44.8554i | 0.544103 | + | 1.60096i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 10.4110i | − | 0.371114i | −0.982634 | − | 0.185557i | \(-0.940591\pi\) | ||
0.982634 | − | 0.185557i | \(-0.0594089\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −57.2561 | −2.03837 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.8703 | 0.813175 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.0867308i | − | 0.00307990i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −41.2918 | + | 14.0335i | −1.46447 | + | 0.497717i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 28.0848i | − | 0.994814i | −0.867517 | − | 0.497407i | \(-0.834286\pi\) | ||
0.867517 | − | 0.497407i | \(-0.165714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.991492 | −0.0350765 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.9975 | 0.777243 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.99008i | − | 0.105517i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.19850 | + | 2.10663i | −0.218468 | + | 0.0742489i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.57550i | 0.0906618i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.1238 | 0.391092 | 0.195546 | − | 0.980695i | \(-0.437352\pi\) | ||||
0.195546 | + | 0.980695i | \(0.437352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.7572 | −1.00980 | −0.504900 | − | 0.863178i | \(-0.668471\pi\) | ||||
−0.504900 | + | 0.863178i | \(0.668471\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.48679i | 0.332716i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.0733 | − | 44.3513i | −0.527994 | − | 1.55356i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 36.2842i | − | 1.26942i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.116886 | 0.00408434 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.0808 | 1.29413 | 0.647064 | − | 0.762435i | \(-0.275996\pi\) | ||||
0.647064 | + | 0.762435i | \(0.275996\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.9501i | − | 0.381698i | −0.981619 | − | 0.190849i | \(-0.938876\pi\) | ||
0.981619 | − | 0.190849i | \(-0.0611241\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 31.2893 | + | 40.7155i | 1.08935 | + | 1.41753i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.9973i | − | 0.486732i | −0.969934 | − | 0.243366i | \(-0.921748\pi\) | ||
0.969934 | − | 0.243366i | \(-0.0782517\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0622 | −0.557864 | −0.278932 | − | 0.960311i | \(-0.589980\pi\) | ||||
−0.278932 | + | 0.960311i | \(0.589980\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.71853 | −0.128995 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.244233i | 0.00846216i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.90487 | − | 23.2591i | −0.273559 | − | 0.804914i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.36017i | 0.0470144i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.49187 | 0.327696 | 0.163848 | − | 0.986486i | \(-0.447609\pi\) | ||||
0.163848 | + | 0.986486i | \(0.447609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.2371 | 0.594381 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.6919i | 0.884876i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.5225 | − | 9.35382i | 0.946802 | − | 0.321781i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 17.2288i | − | 0.591988i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.5575 | 0.396653 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.60741 | 0.157940 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.45965i | − | 0.118456i | −0.998244 | − | 0.0592280i | \(-0.981136\pi\) | ||
0.998244 | − | 0.0592280i | \(-0.0188639\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.7257 | − | 10.1026i | 1.01660 | − | 0.345502i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.729973i | 0.0249354i | 0.999922 | + | 0.0124677i | \(0.00396869\pi\) | ||||
−0.999922 | + | 0.0124677i | \(0.996031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.357241 | −0.0121889 | −0.00609446 | − | 0.999981i | \(-0.501940\pi\) | ||||
−0.00609446 | + | 0.999981i | \(0.501940\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 56.1851 | 1.91478 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 16.8358i | − | 0.573098i | −0.958066 | − | 0.286549i | \(-0.907492\pi\) | ||
0.958066 | − | 0.286549i | \(-0.0925082\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.10198 | − | 9.12720i | −0.105470 | − | 0.310334i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 42.4280i | − | 1.44093i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.7649 | 0.670477 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0899362 | −0.00304737 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.2782i | 1.63397i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.2368 | − | 18.1560i | −0.920772 | − | 0.613784i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 8.06147i | − | 0.272217i | −0.990694 | − | 0.136108i | \(-0.956540\pi\) | ||
0.990694 | − | 0.136108i | \(-0.0434595\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −40.7557 | −1.37466 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.7548 | −1.27199 | −0.635996 | − | 0.771693i | \(-0.719410\pi\) | ||||
−0.635996 | + | 0.771693i | \(0.719410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.2103i | 1.18492i | 0.805600 | + | 0.592460i | \(0.201843\pi\) | ||||
−0.805600 | + | 0.592460i | \(0.798157\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −25.4060 | − | 74.7541i | −0.854014 | − | 2.51283i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.4225i | 0.719297i | 0.933088 | + | 0.359649i | \(0.117103\pi\) | ||||
−0.933088 | + | 0.359649i | \(0.882897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.3166 | 0.748474 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.6924 | 1.12874 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.5967i | 0.923488i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 40.3930 | − | 13.7280i | 1.35019 | − | 0.458877i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0307342i | 0.00102619i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.0080 | 0.500545 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.21251 | −0.0403944 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 61.3930i | − | 2.04303i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.66571 | − | 2.94514i | 0.288058 | − | 0.0978997i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 38.7517i | − | 1.28673i | −0.765560 | − | 0.643364i | \(-0.777538\pi\) | ||
0.765560 | − | 0.643364i | \(-0.222462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.2129 | 1.40012 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.0069 | −1.55741 | −0.778704 | − | 0.627391i | \(-0.784123\pi\) | ||||
−0.778704 | + | 0.627391i | \(0.784123\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 31.8782i | − | 1.05501i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.6836 | − | 37.3200i | −0.419308 | − | 1.23376i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 56.9673i | − | 1.88123i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.2360 | −0.403629 | −0.201814 | − | 0.979424i | \(-0.564684\pi\) | ||||
−0.201814 | + | 0.979424i | \(0.564684\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.2101 | 0.764799 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0718223i | 0.00236406i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0374 | + | 18.2663i | 0.461547 | + | 0.600591i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.03260i | 0.198137i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.0143 | 0.426984 | 0.213492 | − | 0.976945i | \(-0.431516\pi\) | ||||
0.213492 | + | 0.976945i | \(0.431516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.79785 | 0.222790 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 60.9114i | 1.99415i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.459395 | + | 1.35171i | 0.0150238 | + | 0.0442057i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.6856i | 1.26380i | 0.775048 | + | 0.631902i | \(0.217726\pi\) | ||||
−0.775048 | + | 0.631902i | \(0.782274\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.5016 | −1.22382 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.8241 | −1.42862 | −0.714312 | − | 0.699828i | \(-0.753260\pi\) | ||||
−0.714312 | + | 0.699828i | \(0.753260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.67826i | 0.250039i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.81990 | − | 1.29824i | 0.124261 | − | 0.0422316i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.3854i | 1.40984i | 0.709289 | + | 0.704918i | \(0.249016\pi\) | ||||
−0.709289 | + | 0.704918i | \(0.750984\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.00894825 | 0.000290473 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.6133 | −0.636005 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.80245i | 0.0907802i | 0.998969 | + | 0.0453901i | \(0.0144531\pi\) | ||||
−0.998969 | + | 0.0453901i | \(0.985547\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.1481 | − | 4.46853i | 0.425463 | − | 0.144598i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 69.8331i | 2.25738i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −47.7704 | −1.54259 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.1286 | −0.842858 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.53000i | 0.0493036i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.54630 | − | 28.0888i | −0.307306 | − | 0.904211i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30.0015i | − | 0.964783i | −0.875956 | − | 0.482391i | \(-0.839768\pi\) | ||
0.875956 | − | 0.482391i | \(-0.160232\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.67945 | 0.0539518 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.6632 | 1.72213 | 0.861067 | − | 0.508492i | \(-0.169797\pi\) | ||||
0.861067 | + | 0.508492i | \(0.169797\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 58.3474i | − | 1.87053i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.121847 | + | 0.0936380i | −0.00390223 | + | 0.00299882i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 46.4590i | − | 1.48636i | −0.669094 | − | 0.743178i | \(-0.733318\pi\) | ||
0.669094 | − | 0.743178i | \(-0.266682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.8415 | 0.889819 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.94193 | −0.189711 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 50.8346i | − | 1.62137i | −0.585481 | − | 0.810686i | \(-0.699094\pi\) | ||
0.585481 | − | 0.810686i | \(-0.300906\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.98969 | + | 29.3934i | 0.318298 | + | 0.936552i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.6936i | 1.48627i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.38997 | 0.266786 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.30720 | 0.136823 | 0.0684114 | − | 0.997657i | \(-0.478207\pi\) | ||||
0.0684114 | + | 0.997657i | \(0.478207\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 23.1975i | − | 0.736151i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 48.2716 | − | 16.4056i | 1.53031 | − | 0.520094i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.2358i | 0.419181i | 0.977789 | + | 0.209590i | \(0.0672131\pi\) | ||||
−0.977789 | + | 0.209590i | \(0.932787\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.83937 | −0.0898337 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 920.2.e.b.369.2 | ✓ | 14 | |
4.3 | odd | 2 | 1840.2.e.g.369.13 | 14 | |||
5.2 | odd | 4 | 4600.2.a.bi.1.1 | 7 | |||
5.3 | odd | 4 | 4600.2.a.bh.1.7 | 7 | |||
5.4 | even | 2 | inner | 920.2.e.b.369.13 | yes | 14 | |
20.3 | even | 4 | 9200.2.a.dc.1.1 | 7 | |||
20.7 | even | 4 | 9200.2.a.cz.1.7 | 7 | |||
20.19 | odd | 2 | 1840.2.e.g.369.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.2 | ✓ | 14 | 1.1 | even | 1 | trivial | |
920.2.e.b.369.13 | yes | 14 | 5.4 | even | 2 | inner | |
1840.2.e.g.369.2 | 14 | 20.19 | odd | 2 | |||
1840.2.e.g.369.13 | 14 | 4.3 | odd | 2 | |||
4600.2.a.bh.1.7 | 7 | 5.3 | odd | 4 | |||
4600.2.a.bi.1.1 | 7 | 5.2 | odd | 4 | |||
9200.2.a.cz.1.7 | 7 | 20.7 | even | 4 | |||
9200.2.a.dc.1.1 | 7 | 20.3 | even | 4 |